Properties

Label 76.6.e.a.49.1
Level $76$
Weight $6$
Character 76.49
Analytic conductor $12.189$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} - 1275481376 x^{11} + 361098181456 x^{10} - 863969476320 x^{9} + 79755165392064 x^{8} - 375077568148992 x^{7} + 12736924096193536 x^{6} - 57314532742553600 x^{5} + 977121800205220864 x^{4} - 4977732006498379776 x^{3} + 53672321824823513088 x^{2} - 185653809995679793152 x + 804303742853852430336\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{3}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.1
Root \(14.2764 + 24.7275i\) of defining polynomial
Character \(\chi\) \(=\) 76.49
Dual form 76.6.e.a.45.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-14.7764 + 25.5935i) q^{3} +(35.6401 - 61.7304i) q^{5} +252.315 q^{7} +(-315.186 - 545.918i) q^{9} +O(q^{10})\) \(q+(-14.7764 + 25.5935i) q^{3} +(35.6401 - 61.7304i) q^{5} +252.315 q^{7} +(-315.186 - 545.918i) q^{9} +88.0323 q^{11} +(307.862 + 533.232i) q^{13} +(1053.27 + 1824.31i) q^{15} +(285.543 - 494.575i) q^{17} +(361.524 + 1531.47i) q^{19} +(-3728.32 + 6457.64i) q^{21} +(-1214.28 - 2103.20i) q^{23} +(-977.931 - 1693.83i) q^{25} +11447.9 q^{27} +(1142.82 + 1979.43i) q^{29} +3684.20 q^{31} +(-1300.80 + 2253.06i) q^{33} +(8992.54 - 15575.5i) q^{35} +3064.28 q^{37} -18196.4 q^{39} +(-1246.89 + 2159.67i) q^{41} +(-2450.11 + 4243.71i) q^{43} -44933.0 q^{45} +(8786.51 + 15218.7i) q^{47} +46856.0 q^{49} +(8438.61 + 14616.1i) q^{51} +(-12713.9 - 22021.1i) q^{53} +(3137.48 - 5434.27i) q^{55} +(-44537.7 - 13377.0i) q^{57} +(-11756.9 + 20363.5i) q^{59} +(9886.00 + 17123.1i) q^{61} +(-79526.2 - 137743. i) q^{63} +43888.8 q^{65} +(-13694.3 - 23719.2i) q^{67} +71771.0 q^{69} +(-16750.0 + 29011.9i) q^{71} +(-8986.08 + 15564.3i) q^{73} +57801.3 q^{75} +22211.9 q^{77} +(41242.9 - 71434.8i) q^{79} +(-92569.6 + 160335. i) q^{81} +40274.4 q^{83} +(-20353.5 - 35253.4i) q^{85} -67547.4 q^{87} +(-27641.5 - 47876.5i) q^{89} +(77678.2 + 134543. i) q^{91} +(-54439.3 + 94291.7i) q^{93} +(107423. + 32264.7i) q^{95} +(13348.8 - 23120.7i) q^{97} +(-27746.6 - 48058.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −14.7764 + 25.5935i −0.947909 + 1.64183i −0.198088 + 0.980184i \(0.563473\pi\)
−0.749820 + 0.661642i \(0.769860\pi\)
\(4\) 0 0
\(5\) 35.6401 61.7304i 0.637549 1.10427i −0.348420 0.937339i \(-0.613282\pi\)
0.985969 0.166929i \(-0.0533850\pi\)
\(6\) 0 0
\(7\) 252.315 1.94625 0.973125 0.230279i \(-0.0739637\pi\)
0.973125 + 0.230279i \(0.0739637\pi\)
\(8\) 0 0
\(9\) −315.186 545.918i −1.29706 2.24658i
\(10\) 0 0
\(11\) 88.0323 0.219362 0.109681 0.993967i \(-0.465017\pi\)
0.109681 + 0.993967i \(0.465017\pi\)
\(12\) 0 0
\(13\) 307.862 + 533.232i 0.505239 + 0.875100i 0.999982 + 0.00606030i \(0.00192907\pi\)
−0.494742 + 0.869040i \(0.664738\pi\)
\(14\) 0 0
\(15\) 1053.27 + 1824.31i 1.20868 + 2.09349i
\(16\) 0 0
\(17\) 285.543 494.575i 0.239634 0.415059i −0.720975 0.692961i \(-0.756306\pi\)
0.960609 + 0.277902i \(0.0896391\pi\)
\(18\) 0 0
\(19\) 361.524 + 1531.47i 0.229748 + 0.973250i
\(20\) 0 0
\(21\) −3728.32 + 6457.64i −1.84487 + 3.19540i
\(22\) 0 0
\(23\) −1214.28 2103.20i −0.478630 0.829011i 0.521070 0.853514i \(-0.325533\pi\)
−0.999700 + 0.0245027i \(0.992200\pi\)
\(24\) 0 0
\(25\) −977.931 1693.83i −0.312938 0.542024i
\(26\) 0 0
\(27\) 11447.9 3.02216
\(28\) 0 0
\(29\) 1142.82 + 1979.43i 0.252339 + 0.437064i 0.964169 0.265288i \(-0.0854669\pi\)
−0.711830 + 0.702351i \(0.752134\pi\)
\(30\) 0 0
\(31\) 3684.20 0.688555 0.344278 0.938868i \(-0.388124\pi\)
0.344278 + 0.938868i \(0.388124\pi\)
\(32\) 0 0
\(33\) −1300.80 + 2253.06i −0.207935 + 0.360153i
\(34\) 0 0
\(35\) 8992.54 15575.5i 1.24083 2.14918i
\(36\) 0 0
\(37\) 3064.28 0.367980 0.183990 0.982928i \(-0.441099\pi\)
0.183990 + 0.982928i \(0.441099\pi\)
\(38\) 0 0
\(39\) −18196.4 −1.91568
\(40\) 0 0
\(41\) −1246.89 + 2159.67i −0.115842 + 0.200645i −0.918116 0.396311i \(-0.870290\pi\)
0.802274 + 0.596956i \(0.203623\pi\)
\(42\) 0 0
\(43\) −2450.11 + 4243.71i −0.202075 + 0.350005i −0.949197 0.314682i \(-0.898102\pi\)
0.747122 + 0.664687i \(0.231435\pi\)
\(44\) 0 0
\(45\) −44933.0 −3.30776
\(46\) 0 0
\(47\) 8786.51 + 15218.7i 0.580192 + 1.00492i 0.995456 + 0.0952210i \(0.0303558\pi\)
−0.415264 + 0.909701i \(0.636311\pi\)
\(48\) 0 0
\(49\) 46856.0 2.78789
\(50\) 0 0
\(51\) 8438.61 + 14616.1i 0.454303 + 0.786876i
\(52\) 0 0
\(53\) −12713.9 22021.1i −0.621712 1.07684i −0.989167 0.146795i \(-0.953104\pi\)
0.367455 0.930041i \(-0.380229\pi\)
\(54\) 0 0
\(55\) 3137.48 5434.27i 0.139854 0.242234i
\(56\) 0 0
\(57\) −44537.7 13377.0i −1.81569 0.545345i
\(58\) 0 0
\(59\) −11756.9 + 20363.5i −0.439706 + 0.761592i −0.997667 0.0682748i \(-0.978251\pi\)
0.557961 + 0.829867i \(0.311584\pi\)
\(60\) 0 0
\(61\) 9886.00 + 17123.1i 0.340170 + 0.589192i 0.984464 0.175586i \(-0.0561820\pi\)
−0.644294 + 0.764778i \(0.722849\pi\)
\(62\) 0 0
\(63\) −79526.2 137743.i −2.52440 4.37240i
\(64\) 0 0
\(65\) 43888.8 1.28846
\(66\) 0 0
\(67\) −13694.3 23719.2i −0.372694 0.645525i 0.617285 0.786740i \(-0.288233\pi\)
−0.989979 + 0.141214i \(0.954899\pi\)
\(68\) 0 0
\(69\) 71771.0 1.81479
\(70\) 0 0
\(71\) −16750.0 + 29011.9i −0.394339 + 0.683014i −0.993017 0.117975i \(-0.962360\pi\)
0.598678 + 0.800990i \(0.295693\pi\)
\(72\) 0 0
\(73\) −8986.08 + 15564.3i −0.197362 + 0.341841i −0.947672 0.319245i \(-0.896571\pi\)
0.750310 + 0.661086i \(0.229904\pi\)
\(74\) 0 0
\(75\) 57801.3 1.18655
\(76\) 0 0
\(77\) 22211.9 0.426932
\(78\) 0 0
\(79\) 41242.9 71434.8i 0.743501 1.28778i −0.207391 0.978258i \(-0.566497\pi\)
0.950892 0.309523i \(-0.100169\pi\)
\(80\) 0 0
\(81\) −92569.6 + 160335.i −1.56767 + 2.71529i
\(82\) 0 0
\(83\) 40274.4 0.641702 0.320851 0.947130i \(-0.396031\pi\)
0.320851 + 0.947130i \(0.396031\pi\)
\(84\) 0 0
\(85\) −20353.5 35253.4i −0.305557 0.529241i
\(86\) 0 0
\(87\) −67547.4 −0.956777
\(88\) 0 0
\(89\) −27641.5 47876.5i −0.369902 0.640689i 0.619648 0.784880i \(-0.287275\pi\)
−0.989550 + 0.144191i \(0.953942\pi\)
\(90\) 0 0
\(91\) 77678.2 + 134543.i 0.983322 + 1.70316i
\(92\) 0 0
\(93\) −54439.3 + 94291.7i −0.652688 + 1.13049i
\(94\) 0 0
\(95\) 107423. + 32264.7i 1.22120 + 0.366791i
\(96\) 0 0
\(97\) 13348.8 23120.7i 0.144049 0.249501i −0.784968 0.619536i \(-0.787321\pi\)
0.929018 + 0.370035i \(0.120654\pi\)
\(98\) 0 0
\(99\) −27746.6 48058.4i −0.284525 0.492812i
\(100\) 0 0
\(101\) −60668.2 105080.i −0.591777 1.02499i −0.993993 0.109443i \(-0.965093\pi\)
0.402216 0.915545i \(-0.368240\pi\)
\(102\) 0 0
\(103\) −123258. −1.14478 −0.572392 0.819980i \(-0.693985\pi\)
−0.572392 + 0.819980i \(0.693985\pi\)
\(104\) 0 0
\(105\) 265755. + 460302.i 2.35239 + 4.07445i
\(106\) 0 0
\(107\) 225615. 1.90506 0.952529 0.304449i \(-0.0984722\pi\)
0.952529 + 0.304449i \(0.0984722\pi\)
\(108\) 0 0
\(109\) −25583.8 + 44312.5i −0.206253 + 0.357240i −0.950531 0.310629i \(-0.899460\pi\)
0.744279 + 0.667869i \(0.232793\pi\)
\(110\) 0 0
\(111\) −45279.2 + 78425.8i −0.348812 + 0.604160i
\(112\) 0 0
\(113\) −113870. −0.838909 −0.419454 0.907776i \(-0.637779\pi\)
−0.419454 + 0.907776i \(0.637779\pi\)
\(114\) 0 0
\(115\) −173108. −1.22060
\(116\) 0 0
\(117\) 194067. 336134.i 1.31065 2.27012i
\(118\) 0 0
\(119\) 72046.9 124789.i 0.466388 0.807808i
\(120\) 0 0
\(121\) −153301. −0.951881
\(122\) 0 0
\(123\) −36849.1 63824.5i −0.219616 0.380386i
\(124\) 0 0
\(125\) 83336.4 0.477045
\(126\) 0 0
\(127\) −23234.7 40243.6i −0.127828 0.221405i 0.795007 0.606601i \(-0.207467\pi\)
−0.922835 + 0.385196i \(0.874134\pi\)
\(128\) 0 0
\(129\) −72407.6 125414.i −0.383098 0.663546i
\(130\) 0 0
\(131\) 142237. 246361.i 0.724157 1.25428i −0.235163 0.971956i \(-0.575562\pi\)
0.959320 0.282321i \(-0.0911044\pi\)
\(132\) 0 0
\(133\) 91217.9 + 386413.i 0.447148 + 1.89419i
\(134\) 0 0
\(135\) 408006. 706687.i 1.92678 3.33728i
\(136\) 0 0
\(137\) −143955. 249337.i −0.655277 1.13497i −0.981824 0.189792i \(-0.939219\pi\)
0.326547 0.945181i \(-0.394115\pi\)
\(138\) 0 0
\(139\) 88821.1 + 153843.i 0.389923 + 0.675367i 0.992439 0.122740i \(-0.0391681\pi\)
−0.602515 + 0.798107i \(0.705835\pi\)
\(140\) 0 0
\(141\) −519333. −2.19988
\(142\) 0 0
\(143\) 27101.8 + 46941.6i 0.110830 + 0.191963i
\(144\) 0 0
\(145\) 162921. 0.643514
\(146\) 0 0
\(147\) −692365. + 1.19921e6i −2.64266 + 4.57723i
\(148\) 0 0
\(149\) −81129.1 + 140520.i −0.299372 + 0.518527i −0.975992 0.217805i \(-0.930110\pi\)
0.676621 + 0.736332i \(0.263444\pi\)
\(150\) 0 0
\(151\) −449650. −1.60484 −0.802420 0.596760i \(-0.796455\pi\)
−0.802420 + 0.596760i \(0.796455\pi\)
\(152\) 0 0
\(153\) −359996. −1.24328
\(154\) 0 0
\(155\) 131305. 227427.i 0.438988 0.760349i
\(156\) 0 0
\(157\) −27389.5 + 47440.1i −0.0886820 + 0.153602i −0.906954 0.421229i \(-0.861599\pi\)
0.818272 + 0.574831i \(0.194932\pi\)
\(158\) 0 0
\(159\) 751464. 2.35730
\(160\) 0 0
\(161\) −306382. 530669.i −0.931533 1.61346i
\(162\) 0 0
\(163\) 207755. 0.612467 0.306233 0.951956i \(-0.400931\pi\)
0.306233 + 0.951956i \(0.400931\pi\)
\(164\) 0 0
\(165\) 92721.5 + 160598.i 0.265137 + 0.459231i
\(166\) 0 0
\(167\) −136696. 236765.i −0.379284 0.656940i 0.611674 0.791110i \(-0.290496\pi\)
−0.990958 + 0.134170i \(0.957163\pi\)
\(168\) 0 0
\(169\) −3910.94 + 6773.94i −0.0105333 + 0.0182442i
\(170\) 0 0
\(171\) 722110. 680060.i 1.88848 1.77851i
\(172\) 0 0
\(173\) −262508. + 454677.i −0.666848 + 1.15501i 0.311933 + 0.950104i \(0.399024\pi\)
−0.978781 + 0.204910i \(0.934310\pi\)
\(174\) 0 0
\(175\) −246747. 427378.i −0.609055 1.05491i
\(176\) 0 0
\(177\) −347449. 601800.i −0.833601 1.44384i
\(178\) 0 0
\(179\) −13590.9 −0.0317041 −0.0158520 0.999874i \(-0.505046\pi\)
−0.0158520 + 0.999874i \(0.505046\pi\)
\(180\) 0 0
\(181\) −36970.5 64034.9i −0.0838802 0.145285i 0.821033 0.570880i \(-0.193398\pi\)
−0.904913 + 0.425596i \(0.860065\pi\)
\(182\) 0 0
\(183\) −584319. −1.28980
\(184\) 0 0
\(185\) 109211. 189160.i 0.234606 0.406349i
\(186\) 0 0
\(187\) 25137.0 43538.6i 0.0525666 0.0910480i
\(188\) 0 0
\(189\) 2.88849e6 5.88189
\(190\) 0 0
\(191\) −522570. −1.03648 −0.518240 0.855235i \(-0.673413\pi\)
−0.518240 + 0.855235i \(0.673413\pi\)
\(192\) 0 0
\(193\) 12411.0 21496.6i 0.0239836 0.0415409i −0.853784 0.520627i \(-0.825698\pi\)
0.877768 + 0.479086i \(0.159032\pi\)
\(194\) 0 0
\(195\) −648520. + 1.12327e6i −1.22134 + 2.11543i
\(196\) 0 0
\(197\) −363318. −0.666993 −0.333496 0.942751i \(-0.608228\pi\)
−0.333496 + 0.942751i \(0.608228\pi\)
\(198\) 0 0
\(199\) 40673.4 + 70448.5i 0.0728078 + 0.126107i 0.900131 0.435620i \(-0.143471\pi\)
−0.827323 + 0.561726i \(0.810137\pi\)
\(200\) 0 0
\(201\) 809411. 1.41312
\(202\) 0 0
\(203\) 288352. + 499440.i 0.491114 + 0.850635i
\(204\) 0 0
\(205\) 88878.3 + 153942.i 0.147710 + 0.255842i
\(206\) 0 0
\(207\) −765449. + 1.32580e6i −1.24162 + 2.15056i
\(208\) 0 0
\(209\) 31825.8 + 134819.i 0.0503980 + 0.213494i
\(210\) 0 0
\(211\) −235569. + 408017.i −0.364260 + 0.630917i −0.988657 0.150190i \(-0.952011\pi\)
0.624397 + 0.781107i \(0.285345\pi\)
\(212\) 0 0
\(213\) −495011. 857384.i −0.747594 1.29487i
\(214\) 0 0
\(215\) 174644. + 302492.i 0.257666 + 0.446291i
\(216\) 0 0
\(217\) 929580. 1.34010
\(218\) 0 0
\(219\) −265564. 459971.i −0.374162 0.648068i
\(220\) 0 0
\(221\) 351631. 0.484291
\(222\) 0 0
\(223\) −650115. + 1.12603e6i −0.875443 + 1.51631i −0.0191530 + 0.999817i \(0.506097\pi\)
−0.856290 + 0.516495i \(0.827236\pi\)
\(224\) 0 0
\(225\) −616460. + 1.06774e6i −0.811799 + 1.40608i
\(226\) 0 0
\(227\) −73342.4 −0.0944692 −0.0472346 0.998884i \(-0.515041\pi\)
−0.0472346 + 0.998884i \(0.515041\pi\)
\(228\) 0 0
\(229\) −1.25234e6 −1.57809 −0.789046 0.614335i \(-0.789424\pi\)
−0.789046 + 0.614335i \(0.789424\pi\)
\(230\) 0 0
\(231\) −328213. + 568481.i −0.404693 + 0.700949i
\(232\) 0 0
\(233\) 544644. 943351.i 0.657238 1.13837i −0.324089 0.946027i \(-0.605058\pi\)
0.981328 0.192344i \(-0.0616089\pi\)
\(234\) 0 0
\(235\) 1.25261e6 1.47960
\(236\) 0 0
\(237\) 1.21885e6 + 2.11110e6i 1.40954 + 2.44140i
\(238\) 0 0
\(239\) 928359. 1.05129 0.525644 0.850705i \(-0.323825\pi\)
0.525644 + 0.850705i \(0.323825\pi\)
\(240\) 0 0
\(241\) −49744.9 86160.6i −0.0551703 0.0955578i 0.837121 0.547017i \(-0.184237\pi\)
−0.892292 + 0.451460i \(0.850904\pi\)
\(242\) 0 0
\(243\) −1.34477e6 2.32921e6i −1.46094 2.53043i
\(244\) 0 0
\(245\) 1.66995e6 2.89244e6i 1.77742 3.07857i
\(246\) 0 0
\(247\) −705329. + 664256.i −0.735613 + 0.692777i
\(248\) 0 0
\(249\) −595112. + 1.03076e6i −0.608275 + 1.05356i
\(250\) 0 0
\(251\) −190030. 329141.i −0.190387 0.329760i 0.754992 0.655735i \(-0.227641\pi\)
−0.945379 + 0.325975i \(0.894308\pi\)
\(252\) 0 0
\(253\) −106896. 185149.i −0.104993 0.181853i
\(254\) 0 0
\(255\) 1.20301e6 1.15856
\(256\) 0 0
\(257\) −552645. 957209.i −0.521931 0.904012i −0.999675 0.0255121i \(-0.991878\pi\)
0.477743 0.878500i \(-0.341455\pi\)
\(258\) 0 0
\(259\) 773166. 0.716182
\(260\) 0 0
\(261\) 720404. 1.24778e6i 0.654598 1.13380i
\(262\) 0 0
\(263\) −276003. + 478051.i −0.246050 + 0.426172i −0.962426 0.271543i \(-0.912466\pi\)
0.716376 + 0.697714i \(0.245800\pi\)
\(264\) 0 0
\(265\) −1.81250e6 −1.58549
\(266\) 0 0
\(267\) 1.63377e6 1.40253
\(268\) 0 0
\(269\) 859906. 1.48940e6i 0.724553 1.25496i −0.234604 0.972091i \(-0.575379\pi\)
0.959158 0.282872i \(-0.0912872\pi\)
\(270\) 0 0
\(271\) 451795. 782532.i 0.373696 0.647260i −0.616435 0.787406i \(-0.711424\pi\)
0.990131 + 0.140146i \(0.0447571\pi\)
\(272\) 0 0
\(273\) −4.59123e6 −3.72840
\(274\) 0 0
\(275\) −86089.5 149111.i −0.0686465 0.118899i
\(276\) 0 0
\(277\) −1.04518e6 −0.818447 −0.409223 0.912434i \(-0.634200\pi\)
−0.409223 + 0.912434i \(0.634200\pi\)
\(278\) 0 0
\(279\) −1.16121e6 2.01127e6i −0.893099 1.54689i
\(280\) 0 0
\(281\) −213159. 369202.i −0.161041 0.278932i 0.774201 0.632940i \(-0.218152\pi\)
−0.935242 + 0.354008i \(0.884819\pi\)
\(282\) 0 0
\(283\) −29882.7 + 51758.4i −0.0221796 + 0.0384162i −0.876902 0.480669i \(-0.840394\pi\)
0.854723 + 0.519085i \(0.173727\pi\)
\(284\) 0 0
\(285\) −2.41310e6 + 2.27258e6i −1.75980 + 1.65732i
\(286\) 0 0
\(287\) −314609. + 544918.i −0.225458 + 0.390505i
\(288\) 0 0
\(289\) 546859. + 947188.i 0.385151 + 0.667101i
\(290\) 0 0
\(291\) 394494. + 683284.i 0.273092 + 0.473008i
\(292\) 0 0
\(293\) 1.17326e6 0.798410 0.399205 0.916862i \(-0.369286\pi\)
0.399205 + 0.916862i \(0.369286\pi\)
\(294\) 0 0
\(295\) 838032. + 1.45151e6i 0.560668 + 0.971105i
\(296\) 0 0
\(297\) 1.00779e6 0.662947
\(298\) 0 0
\(299\) 747661. 1.29499e6i 0.483645 0.837698i
\(300\) 0 0
\(301\) −618199. + 1.07075e6i −0.393289 + 0.681197i
\(302\) 0 0
\(303\) 3.58584e6 2.24380
\(304\) 0 0
\(305\) 1.40935e6 0.867501
\(306\) 0 0
\(307\) −252040. + 436545.i −0.152624 + 0.264353i −0.932191 0.361966i \(-0.882106\pi\)
0.779567 + 0.626318i \(0.215439\pi\)
\(308\) 0 0
\(309\) 1.82132e6 3.15462e6i 1.08515 1.87954i
\(310\) 0 0
\(311\) 2.39525e6 1.40426 0.702132 0.712046i \(-0.252231\pi\)
0.702132 + 0.712046i \(0.252231\pi\)
\(312\) 0 0
\(313\) −1.06455e6 1.84385e6i −0.614193 1.06381i −0.990525 0.137329i \(-0.956148\pi\)
0.376332 0.926485i \(-0.377185\pi\)
\(314\) 0 0
\(315\) −1.13373e7 −6.43773
\(316\) 0 0
\(317\) −399285. 691581.i −0.223169 0.386541i 0.732599 0.680660i \(-0.238307\pi\)
−0.955769 + 0.294120i \(0.904974\pi\)
\(318\) 0 0
\(319\) 100605. + 174254.i 0.0553535 + 0.0958750i
\(320\) 0 0
\(321\) −3.33378e6 + 5.77428e6i −1.80582 + 3.12777i
\(322\) 0 0
\(323\) 860657. + 258500.i 0.459012 + 0.137865i
\(324\) 0 0
\(325\) 602135. 1.04293e6i 0.316217 0.547704i
\(326\) 0 0
\(327\) −756075. 1.30956e6i −0.391017 0.677261i
\(328\) 0 0
\(329\) 2.21697e6 + 3.83991e6i 1.12920 + 1.95583i
\(330\) 0 0
\(331\) −224790. −0.112773 −0.0563867 0.998409i \(-0.517958\pi\)
−0.0563867 + 0.998409i \(0.517958\pi\)
\(332\) 0 0
\(333\) −965819. 1.67285e6i −0.477293 0.826696i
\(334\) 0 0
\(335\) −1.95226e6 −0.950444
\(336\) 0 0
\(337\) 1.02795e6 1.78046e6i 0.493056 0.853998i −0.506912 0.861998i \(-0.669213\pi\)
0.999968 + 0.00799964i \(0.00254639\pi\)
\(338\) 0 0
\(339\) 1.68260e6 2.91435e6i 0.795209 1.37734i
\(340\) 0 0
\(341\) 324329. 0.151043
\(342\) 0 0
\(343\) 7.58183e6 3.47967
\(344\) 0 0
\(345\) 2.55792e6 4.43046e6i 1.15702 2.00401i
\(346\) 0 0
\(347\) −1.48248e6 + 2.56773e6i −0.660946 + 1.14479i 0.319422 + 0.947613i \(0.396511\pi\)
−0.980368 + 0.197179i \(0.936822\pi\)
\(348\) 0 0
\(349\) 2.25013e6 0.988883 0.494441 0.869211i \(-0.335373\pi\)
0.494441 + 0.869211i \(0.335373\pi\)
\(350\) 0 0
\(351\) 3.52438e6 + 6.10441e6i 1.52692 + 2.64470i
\(352\) 0 0
\(353\) −1.72711e6 −0.737706 −0.368853 0.929488i \(-0.620249\pi\)
−0.368853 + 0.929488i \(0.620249\pi\)
\(354\) 0 0
\(355\) 1.19394e6 + 2.06797e6i 0.502820 + 0.870910i
\(356\) 0 0
\(357\) 2.12919e6 + 3.68787e6i 0.884187 + 1.53146i
\(358\) 0 0
\(359\) −526967. + 912734.i −0.215798 + 0.373773i −0.953519 0.301332i \(-0.902569\pi\)
0.737721 + 0.675106i \(0.235902\pi\)
\(360\) 0 0
\(361\) −2.21470e6 + 1.10732e6i −0.894431 + 0.447205i
\(362\) 0 0
\(363\) 2.26525e6 3.92352e6i 0.902296 1.56282i
\(364\) 0 0
\(365\) 640529. + 1.10943e6i 0.251656 + 0.435881i
\(366\) 0 0
\(367\) −1.90021e6 3.29126e6i −0.736438 1.27555i −0.954089 0.299522i \(-0.903173\pi\)
0.217651 0.976027i \(-0.430160\pi\)
\(368\) 0 0
\(369\) 1.57200e6 0.601018
\(370\) 0 0
\(371\) −3.20791e6 5.55627e6i −1.21001 2.09579i
\(372\) 0 0
\(373\) −1.16264e6 −0.432685 −0.216342 0.976318i \(-0.569413\pi\)
−0.216342 + 0.976318i \(0.569413\pi\)
\(374\) 0 0
\(375\) −1.23141e6 + 2.13287e6i −0.452195 + 0.783225i
\(376\) 0 0
\(377\) −703663. + 1.21878e6i −0.254983 + 0.441643i
\(378\) 0 0
\(379\) −1.49509e6 −0.534648 −0.267324 0.963607i \(-0.586139\pi\)
−0.267324 + 0.963607i \(0.586139\pi\)
\(380\) 0 0
\(381\) 1.37330e6 0.484678
\(382\) 0 0
\(383\) −2.52086e6 + 4.36626e6i −0.878115 + 1.52094i −0.0247088 + 0.999695i \(0.507866\pi\)
−0.853407 + 0.521246i \(0.825467\pi\)
\(384\) 0 0
\(385\) 791634. 1.37115e6i 0.272190 0.471448i
\(386\) 0 0
\(387\) 3.08895e6 1.04842
\(388\) 0 0
\(389\) 612495. + 1.06087e6i 0.205224 + 0.355459i 0.950204 0.311628i \(-0.100874\pi\)
−0.744980 + 0.667087i \(0.767541\pi\)
\(390\) 0 0
\(391\) −1.38692e6 −0.458785
\(392\) 0 0
\(393\) 4.20350e6 + 7.28067e6i 1.37287 + 2.37788i
\(394\) 0 0
\(395\) −2.93980e6 5.09188e6i −0.948036 1.64205i
\(396\) 0 0
\(397\) −639677. + 1.10795e6i −0.203697 + 0.352813i −0.949717 0.313110i \(-0.898629\pi\)
0.746020 + 0.665924i \(0.231962\pi\)
\(398\) 0 0
\(399\) −1.12376e7 3.37522e6i −3.53378 1.06138i
\(400\) 0 0
\(401\) −473386. + 819928.i −0.147013 + 0.254633i −0.930122 0.367251i \(-0.880299\pi\)
0.783109 + 0.621884i \(0.213632\pi\)
\(402\) 0 0
\(403\) 1.13422e6 + 1.96453e6i 0.347885 + 0.602555i
\(404\) 0 0
\(405\) 6.59838e6 + 1.14287e7i 1.99894 + 3.46226i
\(406\) 0 0
\(407\) 269756. 0.0807208
\(408\) 0 0
\(409\) −1.78713e6 3.09540e6i −0.528260 0.914974i −0.999457 0.0329456i \(-0.989511\pi\)
0.471197 0.882028i \(-0.343822\pi\)
\(410\) 0 0
\(411\) 8.50856e6 2.48457
\(412\) 0 0
\(413\) −2.96644e6 + 5.13803e6i −0.855777 + 1.48225i
\(414\) 0 0
\(415\) 1.43538e6 2.48616e6i 0.409117 0.708611i
\(416\) 0 0
\(417\) −5.24984e6 −1.47845
\(418\) 0 0
\(419\) −4.64582e6 −1.29279 −0.646395 0.763003i \(-0.723724\pi\)
−0.646395 + 0.763003i \(0.723724\pi\)
\(420\) 0 0
\(421\) 1.59986e6 2.77104e6i 0.439923 0.761970i −0.557760 0.830002i \(-0.688339\pi\)
0.997683 + 0.0680329i \(0.0216723\pi\)
\(422\) 0 0
\(423\) 5.53877e6 9.59342e6i 1.50509 2.60689i
\(424\) 0 0
\(425\) −1.11697e6 −0.299963
\(426\) 0 0
\(427\) 2.49439e6 + 4.32041e6i 0.662056 + 1.14671i
\(428\) 0 0
\(429\) −1.60187e6 −0.420227
\(430\) 0 0
\(431\) 2.46054e6 + 4.26178e6i 0.638025 + 1.10509i 0.985866 + 0.167537i \(0.0535815\pi\)
−0.347841 + 0.937553i \(0.613085\pi\)
\(432\) 0 0
\(433\) 1.48931e6 + 2.57956e6i 0.381738 + 0.661189i 0.991311 0.131541i \(-0.0419924\pi\)
−0.609573 + 0.792730i \(0.708659\pi\)
\(434\) 0 0
\(435\) −2.40740e6 + 4.16973e6i −0.609992 + 1.05654i
\(436\) 0 0
\(437\) 2.78199e6 2.61999e6i 0.696871 0.656291i
\(438\) 0 0
\(439\) 1.08758e6 1.88374e6i 0.269339 0.466509i −0.699352 0.714777i \(-0.746528\pi\)
0.968691 + 0.248268i \(0.0798614\pi\)
\(440\) 0 0
\(441\) −1.47684e7 2.55795e7i −3.61606 6.26320i
\(442\) 0 0
\(443\) −189407. 328062.i −0.0458549 0.0794231i 0.842187 0.539186i \(-0.181268\pi\)
−0.888042 + 0.459763i \(0.847935\pi\)
\(444\) 0 0
\(445\) −3.94058e6 −0.943323
\(446\) 0 0
\(447\) −2.39760e6 4.15276e6i −0.567554 0.983032i
\(448\) 0 0
\(449\) −5.64067e6 −1.32043 −0.660214 0.751077i \(-0.729534\pi\)
−0.660214 + 0.751077i \(0.729534\pi\)
\(450\) 0 0
\(451\) −109766. + 190121.i −0.0254114 + 0.0440138i
\(452\) 0 0
\(453\) 6.64422e6 1.15081e7i 1.52124 2.63487i
\(454\) 0 0
\(455\) 1.10738e7 2.50766
\(456\) 0 0
\(457\) −317551. −0.0711252 −0.0355626 0.999367i \(-0.511322\pi\)
−0.0355626 + 0.999367i \(0.511322\pi\)
\(458\) 0 0
\(459\) 3.26888e6 5.66187e6i 0.724215 1.25438i
\(460\) 0 0
\(461\) 1.63141e6 2.82569e6i 0.357529 0.619259i −0.630018 0.776580i \(-0.716953\pi\)
0.987547 + 0.157322i \(0.0502859\pi\)
\(462\) 0 0
\(463\) −7.65368e6 −1.65927 −0.829636 0.558305i \(-0.811452\pi\)
−0.829636 + 0.558305i \(0.811452\pi\)
\(464\) 0 0
\(465\) 3.88044e6 + 6.72113e6i 0.832241 + 1.44148i
\(466\) 0 0
\(467\) 885237. 0.187831 0.0939155 0.995580i \(-0.470062\pi\)
0.0939155 + 0.995580i \(0.470062\pi\)
\(468\) 0 0
\(469\) −3.45528e6 5.98472e6i −0.725356 1.25635i
\(470\) 0 0
\(471\) −809439. 1.40199e6i −0.168125 0.291201i
\(472\) 0 0
\(473\) −215689. + 373583.i −0.0443276 + 0.0767777i
\(474\) 0 0
\(475\) 2.24050e6 2.11003e6i 0.455628 0.429096i
\(476\) 0 0
\(477\) −8.01448e6 + 1.38815e7i −1.61280 + 2.79345i
\(478\) 0 0
\(479\) 2.58332e6 + 4.47445e6i 0.514447 + 0.891047i 0.999859 + 0.0167625i \(0.00533592\pi\)
−0.485413 + 0.874285i \(0.661331\pi\)
\(480\) 0 0
\(481\) 943375. + 1.63397e6i 0.185918 + 0.322020i
\(482\) 0 0
\(483\) 1.81089e7 3.53203
\(484\) 0 0
\(485\) −951502. 1.64805e6i −0.183677 0.318138i
\(486\) 0 0
\(487\) −4.53740e6 −0.866931 −0.433465 0.901170i \(-0.642709\pi\)
−0.433465 + 0.901170i \(0.642709\pi\)
\(488\) 0 0
\(489\) −3.06988e6 + 5.31719e6i −0.580563 + 1.00556i
\(490\) 0 0
\(491\) −4.58323e6 + 7.93839e6i −0.857963 + 1.48603i 0.0159066 + 0.999873i \(0.494937\pi\)
−0.873869 + 0.486161i \(0.838397\pi\)
\(492\) 0 0
\(493\) 1.30530e6 0.241876
\(494\) 0 0
\(495\) −3.95556e6 −0.725596
\(496\) 0 0
\(497\) −4.22628e6 + 7.32014e6i −0.767481 + 1.32932i
\(498\) 0 0
\(499\) −4.86531e6 + 8.42697e6i −0.874700 + 1.51503i −0.0176190 + 0.999845i \(0.505609\pi\)
−0.857081 + 0.515181i \(0.827725\pi\)
\(500\) 0 0
\(501\) 8.07952e6 1.43811
\(502\) 0 0
\(503\) −5.37084e6 9.30257e6i −0.946503 1.63939i −0.752713 0.658349i \(-0.771255\pi\)
−0.193791 0.981043i \(-0.562078\pi\)
\(504\) 0 0
\(505\) −8.64888e6 −1.50915
\(506\) 0 0
\(507\) −115579. 200189.i −0.0199692 0.0345876i
\(508\) 0 0
\(509\) −2.77946e6 4.81416e6i −0.475516 0.823618i 0.524090 0.851663i \(-0.324405\pi\)
−0.999607 + 0.0280444i \(0.991072\pi\)
\(510\) 0 0
\(511\) −2.26733e6 + 3.92712e6i −0.384115 + 0.665307i
\(512\) 0 0
\(513\) 4.13870e6 + 1.75322e7i 0.694338 + 2.94132i
\(514\) 0 0
\(515\) −4.39294e6 + 7.60880e6i −0.729856 + 1.26415i
\(516\) 0 0
\(517\) 773497. + 1.33974e6i 0.127272 + 0.220441i
\(518\) 0 0
\(519\) −7.75785e6 1.34370e7i −1.26422 2.18970i
\(520\) 0 0
\(521\) −2.44377e6 −0.394427 −0.197213 0.980361i \(-0.563189\pi\)
−0.197213 + 0.980361i \(0.563189\pi\)
\(522\) 0 0
\(523\) 2.06842e6 + 3.58260e6i 0.330662 + 0.572723i 0.982642 0.185513i \(-0.0593948\pi\)
−0.651980 + 0.758236i \(0.726061\pi\)
\(524\) 0 0
\(525\) 1.45842e7 2.30931
\(526\) 0 0
\(527\) 1.05200e6 1.82211e6i 0.165002 0.285791i
\(528\) 0 0
\(529\) 269211. 466288.i 0.0418268 0.0724461i
\(530\) 0 0
\(531\) 1.48224e7 2.28130
\(532\) 0 0
\(533\) −1.53547e6 −0.234112
\(534\) 0 0
\(535\) 8.04093e6 1.39273e7i 1.21457 2.10369i
\(536\) 0 0
\(537\) 200825. 347839.i 0.0300526 0.0520526i
\(538\) 0 0
\(539\) 4.12485e6 0.611555
\(540\) 0 0
\(541\) 332076. + 575172.i 0.0487803 + 0.0844899i 0.889385 0.457160i \(-0.151133\pi\)
−0.840604 + 0.541650i \(0.817800\pi\)
\(542\) 0 0
\(543\) 2.18517e6 0.318043
\(544\) 0 0
\(545\) 1.82362e6 + 3.15860e6i 0.262992 + 0.455516i
\(546\) 0 0
\(547\) −2.27290e6 3.93678e6i −0.324797 0.562565i 0.656674 0.754174i \(-0.271963\pi\)
−0.981471 + 0.191609i \(0.938629\pi\)
\(548\) 0 0
\(549\) 6.23186e6 1.07939e7i 0.882443 1.52844i
\(550\) 0 0
\(551\) −2.61828e6 + 2.46581e6i −0.367398 + 0.346004i
\(552\) 0 0
\(553\) 1.04062e7 1.80241e7i 1.44704 2.50634i
\(554\) 0 0
\(555\) 3.22751e6 + 5.59021e6i 0.444769 + 0.770363i
\(556\) 0 0
\(557\) 4.10469e6 + 7.10954e6i 0.560586 + 0.970964i 0.997445 + 0.0714342i \(0.0227576\pi\)
−0.436859 + 0.899530i \(0.643909\pi\)
\(558\) 0 0
\(559\) −3.01717e6 −0.408386
\(560\) 0 0
\(561\) 742871. + 1.28669e6i 0.0996566 + 0.172610i
\(562\) 0 0
\(563\) −1.32458e7 −1.76119 −0.880597 0.473866i \(-0.842858\pi\)
−0.880597 + 0.473866i \(0.842858\pi\)
\(564\) 0 0
\(565\) −4.05835e6 + 7.02927e6i −0.534846 + 0.926380i
\(566\) 0 0
\(567\) −2.33567e7 + 4.04550e7i −3.05109 + 5.28464i
\(568\) 0 0
\(569\) 1.11112e7 1.43873 0.719365 0.694632i \(-0.244433\pi\)
0.719365 + 0.694632i \(0.244433\pi\)
\(570\) 0 0
\(571\) 1.44176e7 1.85055 0.925277 0.379291i \(-0.123832\pi\)
0.925277 + 0.379291i \(0.123832\pi\)
\(572\) 0 0
\(573\) 7.72172e6 1.33744e7i 0.982489 1.70172i
\(574\) 0 0
\(575\) −2.37497e6 + 4.11356e6i −0.299563 + 0.518858i
\(576\) 0 0
\(577\) −4.63470e6 −0.579538 −0.289769 0.957097i \(-0.593578\pi\)
−0.289769 + 0.957097i \(0.593578\pi\)
\(578\) 0 0
\(579\) 366782. + 635285.i 0.0454686 + 0.0787539i
\(580\) 0 0
\(581\) 1.01618e7 1.24891
\(582\) 0 0
\(583\) −1.11923e6 1.93857e6i −0.136380 0.236217i
\(584\) 0 0
\(585\) −1.38331e7 2.39597e7i −1.67121 2.89462i
\(586\) 0 0
\(587\) −87378.3 + 151344.i −0.0104667 + 0.0181288i −0.871211 0.490908i \(-0.836665\pi\)
0.860745 + 0.509037i \(0.169998\pi\)
\(588\) 0 0
\(589\) 1.33193e6 + 5.64224e6i 0.158195 + 0.670137i
\(590\) 0 0
\(591\) 5.36854e6 9.29858e6i 0.632248 1.09509i
\(592\) 0 0
\(593\) 63610.1 + 110176.i 0.00742830 + 0.0128662i 0.869716 0.493553i \(-0.164302\pi\)
−0.862287 + 0.506419i \(0.830969\pi\)
\(594\) 0 0
\(595\) −5.13551e6 8.89497e6i −0.594691 1.03003i
\(596\) 0 0
\(597\) −2.40403e6 −0.276061
\(598\) 0 0
\(599\) 8.00216e6 + 1.38601e7i 0.911255 + 1.57834i 0.812293 + 0.583249i \(0.198219\pi\)
0.0989618 + 0.995091i \(0.468448\pi\)
\(600\) 0 0
\(601\) 1.52423e7 1.72134 0.860668 0.509166i \(-0.170046\pi\)
0.860668 + 0.509166i \(0.170046\pi\)
\(602\) 0 0
\(603\) −8.63250e6 + 1.49519e7i −0.966815 + 1.67457i
\(604\) 0 0
\(605\) −5.46367e6 + 9.46336e6i −0.606871 + 1.05113i
\(606\) 0 0
\(607\) 1.49576e7 1.64774 0.823870 0.566778i \(-0.191810\pi\)
0.823870 + 0.566778i \(0.191810\pi\)
\(608\) 0 0
\(609\) −1.70432e7 −1.86213
\(610\) 0 0
\(611\) −5.41005e6 + 9.37049e6i −0.586271 + 1.01545i
\(612\) 0 0
\(613\) 889245. 1.54022e6i 0.0955807 0.165551i −0.814270 0.580486i \(-0.802863\pi\)
0.909851 + 0.414936i \(0.136196\pi\)
\(614\) 0 0
\(615\) −5.25322e6 −0.560064
\(616\) 0 0
\(617\) 7.97293e6 + 1.38095e7i 0.843150 + 1.46038i 0.887218 + 0.461350i \(0.152635\pi\)
−0.0440683 + 0.999029i \(0.514032\pi\)
\(618\) 0 0
\(619\) −1.53524e7 −1.61046 −0.805231 0.592962i \(-0.797959\pi\)
−0.805231 + 0.592962i \(0.797959\pi\)
\(620\) 0 0
\(621\) −1.39010e7 2.40773e7i −1.44650 2.50541i
\(622\) 0 0
\(623\) −6.97438e6 1.20800e7i −0.719922 1.24694i
\(624\) 0 0
\(625\) 6.02615e6 1.04376e7i 0.617078 1.06881i
\(626\) 0 0
\(627\) −3.92076e6 1.17761e6i −0.398292 0.119628i
\(628\) 0 0
\(629\) 874985. 1.51552e6i 0.0881807 0.152734i
\(630\) 0 0
\(631\) 1.84277e6 + 3.19177e6i 0.184246 + 0.319123i 0.943322 0.331879i \(-0.107682\pi\)
−0.759076 + 0.651002i \(0.774349\pi\)
\(632\) 0 0
\(633\) −6.96173e6 1.20581e7i −0.690570 1.19610i
\(634\) 0 0
\(635\) −3.31234e6 −0.325988
\(636\) 0 0
\(637\) 1.44252e7 + 2.49851e7i 1.40855 + 2.43968i
\(638\) 0 0
\(639\) 2.11175e7 2.04592
\(640\) 0 0
\(641\) 2.60486e6 4.51176e6i 0.250403 0.433711i −0.713234 0.700926i \(-0.752770\pi\)
0.963637 + 0.267215i \(0.0861035\pi\)
\(642\) 0 0
\(643\) 3.62947e6 6.28642e6i 0.346191 0.599620i −0.639379 0.768892i \(-0.720808\pi\)
0.985569 + 0.169272i \(0.0541417\pi\)
\(644\) 0 0
\(645\) −1.03225e7 −0.976976
\(646\) 0 0
\(647\) −8.49406e6 −0.797728 −0.398864 0.917010i \(-0.630595\pi\)
−0.398864 + 0.917010i \(0.630595\pi\)
\(648\) 0 0
\(649\) −1.03499e6 + 1.79265e6i −0.0964545 + 0.167064i
\(650\) 0 0
\(651\) −1.37359e7 + 2.37912e7i −1.27029 + 2.20021i
\(652\) 0 0
\(653\) −1.16393e7 −1.06818 −0.534089 0.845428i \(-0.679345\pi\)
−0.534089 + 0.845428i \(0.679345\pi\)
\(654\) 0 0
\(655\) −1.01386e7 1.75606e7i −0.923372 1.59933i
\(656\) 0 0
\(657\) 1.13291e7 1.02396
\(658\) 0 0
\(659\) −9.86735e6 1.70907e7i −0.885089 1.53302i −0.845612 0.533798i \(-0.820764\pi\)
−0.0394769 0.999220i \(-0.512569\pi\)
\(660\) 0 0
\(661\) 7.97821e6 + 1.38187e7i 0.710235 + 1.23016i 0.964769 + 0.263099i \(0.0847446\pi\)
−0.254534 + 0.967064i \(0.581922\pi\)
\(662\) 0 0
\(663\) −5.19585e6 + 8.99947e6i −0.459063 + 0.795121i
\(664\) 0 0
\(665\) 2.71045e7 + 8.14088e6i 2.37677 + 0.713867i
\(666\) 0 0
\(667\) 2.77542e6 4.80717e6i 0.241554 0.418384i
\(668\) 0 0
\(669\) −1.92128e7 3.32775e7i −1.65968 2.87465i
\(670\) 0 0
\(671\) 870288. + 1.50738e6i 0.0746202 + 0.129246i
\(672\) 0 0
\(673\) 1.18685e7 1.01008 0.505041 0.863096i \(-0.331477\pi\)
0.505041 + 0.863096i \(0.331477\pi\)
\(674\) 0 0
\(675\) −1.11953e7 1.93908e7i −0.945750 1.63809i
\(676\) 0 0
\(677\) −1.13643e7 −0.952952 −0.476476 0.879188i \(-0.658086\pi\)
−0.476476 + 0.879188i \(0.658086\pi\)
\(678\) 0 0
\(679\) 3.36810e6 5.83372e6i 0.280356 0.485591i
\(680\) 0 0
\(681\) 1.08374e6 1.87709e6i 0.0895482 0.155102i
\(682\) 0 0
\(683\) 1.33134e7 1.09204 0.546018 0.837774i \(-0.316143\pi\)
0.546018 + 0.837774i \(0.316143\pi\)
\(684\) 0 0
\(685\) −2.05223e7 −1.67109
\(686\) 0 0
\(687\) 1.85051e7 3.20517e7i 1.49589 2.59095i
\(688\) 0 0
\(689\) 7.82824e6 1.35589e7i 0.628226 1.08812i
\(690\) 0 0
\(691\) 1.77578e7 1.41480 0.707400 0.706813i \(-0.249868\pi\)
0.707400 + 0.706813i \(0.249868\pi\)
\(692\) 0 0
\(693\) −7.00088e6 1.21259e7i −0.553757 0.959136i
\(694\) 0 0
\(695\) 1.26624e7 0.994381
\(696\) 0 0
\(697\) 712079. + 1.23336e6i 0.0555196 + 0.0961628i
\(698\) 0 0
\(699\) 1.60958e7 + 2.78787e7i 1.24600 + 2.15814i
\(700\) 0 0
\(701\) 2.58452e6 4.47652e6i 0.198648 0.344069i −0.749442 0.662070i \(-0.769678\pi\)
0.948090 + 0.318001i \(0.103012\pi\)
\(702\) 0 0
\(703\) 1.10781e6 + 4.69286e6i 0.0845429 + 0.358137i
\(704\) 0 0
\(705\) −1.85091e7 + 3.20586e7i −1.40253 + 2.42925i
\(706\) 0 0
\(707\) −1.53075e7 2.65134e7i −1.15175 1.99488i
\(708\) 0 0
\(709\) 6.35081e6 + 1.09999e7i 0.474476 + 0.821816i 0.999573 0.0292265i \(-0.00930441\pi\)
−0.525097 + 0.851042i \(0.675971\pi\)
\(710\) 0 0
\(711\) −5.19967e7 −3.85746
\(712\) 0 0
\(713\) −4.47366e6 7.74860e6i −0.329563 0.570820i
\(714\) 0 0
\(715\) 3.86364e6 0.282638
\(716\) 0 0
\(717\) −1.37178e7 + 2.37600e7i −0.996524 + 1.72603i
\(718\) 0 0
\(719\) 1.17643e7 2.03763e7i 0.848678 1.46995i −0.0337101 0.999432i \(-0.510732\pi\)
0.882388 0.470522i \(-0.155934\pi\)
\(720\) 0 0
\(721\) −3.11000e7 −2.22804
\(722\) 0 0
\(723\) 2.94021e6 0.209186
\(724\) 0 0
\(725\) 2.23520e6 3.87149e6i 0.157933 0.273548i
\(726\) 0 0
\(727\) 1.08765e7 1.88387e7i 0.763229 1.32195i −0.177949 0.984040i \(-0.556946\pi\)
0.941178 0.337911i \(-0.109720\pi\)
\(728\) 0 0
\(729\) 3.44949e7 2.40401
\(730\) 0 0
\(731\) 1.39922e6 + 2.42352e6i 0.0968485 + 0.167746i
\(732\) 0 0
\(733\) −9.80139e6 −0.673795 −0.336897 0.941541i \(-0.609378\pi\)
−0.336897 + 0.941541i \(0.609378\pi\)
\(734\) 0 0
\(735\) 4.93519e7 + 8.54800e7i 3.36965 + 5.83641i
\(736\) 0 0
\(737\) −1.20554e6 2.08806e6i −0.0817548 0.141603i
\(738\) 0 0
\(739\) −7.08883e6 + 1.22782e7i −0.477489 + 0.827035i −0.999667 0.0258011i \(-0.991786\pi\)
0.522178 + 0.852837i \(0.325120\pi\)
\(740\) 0 0
\(741\) −6.57842e6 2.78672e7i −0.440125 1.86444i
\(742\) 0 0
\(743\) −3.04168e6 + 5.26834e6i −0.202135 + 0.350108i −0.949216 0.314625i \(-0.898121\pi\)
0.747081 + 0.664733i \(0.231455\pi\)
\(744\) 0 0
\(745\) 5.78289e6 + 1.00163e7i 0.381728 + 0.661173i
\(746\) 0 0
\(747\) −1.26939e7 2.19865e7i −0.832327 1.44163i
\(748\) 0 0
\(749\) 5.69261e7 3.70772
\(750\) 0 0
\(751\) 6.05235e6 + 1.04830e7i 0.391584 + 0.678243i 0.992659 0.120950i \(-0.0385941\pi\)
−0.601075 + 0.799193i \(0.705261\pi\)
\(752\) 0 0
\(753\) 1.12318e7 0.721878
\(754\) 0 0
\(755\) −1.60255e7 + 2.77571e7i −1.02316 + 1.77217i
\(756\) 0 0
\(757\) −837126. + 1.44994e6i −0.0530947 + 0.0919627i −0.891351 0.453313i \(-0.850242\pi\)
0.838257 + 0.545276i \(0.183575\pi\)
\(758\) 0 0
\(759\) 6.31817e6 0.398095
\(760\) 0 0
\(761\) −1.71108e7 −1.07105 −0.535525 0.844520i \(-0.679886\pi\)
−0.535525 + 0.844520i \(0.679886\pi\)
\(762\) 0 0
\(763\) −6.45519e6 + 1.11807e7i −0.401419 + 0.695278i
\(764\) 0 0
\(765\) −1.28303e7 + 2.22227e7i −0.792653 + 1.37292i
\(766\) 0 0
\(767\) −1.44780e7 −0.888626
\(768\) 0 0
\(769\) −4.88795e6 8.46617e6i −0.298065 0.516263i 0.677628 0.735404i \(-0.263008\pi\)
−0.975693 + 0.219141i \(0.929674\pi\)
\(770\) 0 0
\(771\) 3.26645e7 1.97897
\(772\) 0 0
\(773\) −6.30084e6 1.09134e7i −0.379271 0.656916i 0.611686 0.791101i \(-0.290492\pi\)
−0.990956 + 0.134185i \(0.957158\pi\)
\(774\) 0 0
\(775\) −3.60289e6 6.24039e6i −0.215475 0.373214i
\(776\) 0 0
\(777\) −1.14246e7 + 1.97880e7i −0.678875 + 1.17585i
\(778\) 0 0
\(779\) −3.75825e6 1.12880e6i −0.221892 0.0666457i
\(780\) 0 0
\(781\) −1.47454e6 + 2.55398e6i −0.0865027 + 0.149827i
\(782\) 0 0
\(783\) 1.30830e7 + 2.26604e7i 0.762610 + 1.32088i
\(784\) 0 0
\(785\) 1.95233e6 + 3.38154e6i 0.113078 + 0.195857i
\(786\) 0 0
\(787\) −1.91406e7 −1.10159 −0.550795 0.834641i \(-0.685675\pi\)
−0.550795 + 0.834641i \(0.685675\pi\)
\(788\) 0 0
\(789\) −8.15667e6 1.41278e7i